The Clone fits into the line of succession just like any other child, based on the specific inheritance rules of that society.

A Clone will be like an identical twin (which is really what an identical twin is..) so they will not be 100.000000000% identical to the progenator. They will have different fingerprints for example...

They will also have their own personality, they may have some traits in common with their progenator, but the old Nature/Nurture argument comes into play. Reality is that a person is shaped by both Nature (genetics) and Nurture (environment) and so the clone will be a unique person.

The Regina nobles in the spinward marches are officially stated as raising clones of themselves as their children and inheritor for centuries. They have developed a process the neutralizes the sex determination so the the clone can develop as either male or female but is otherwise a clone of the original. This is from the OTU both Megatraveller and TNE. Does any other world do something similar I’m not sure

Short answer: a clone counts as a younger sibling of the genetic donor.

Longer answer: Generally a clone (commonly called a true-child) in most cases is treated like a younger sibling for the purposes of inheritance. Free clones, like Seldarian, are those independent to develop their own personalities. In one case in GT: Nobles, it is mentioned that a title in the Solomani Rim is preferentially passed to clones over naturally conceived children.

As for the biotech end of it, I would suppose that it would be easy for geneticists at Imperial Tech Levels to take a donor's genetic material and replace one sex determination chromosome with another, preferably from a related party. It also sounds like the genetic aging items may be fixed as well.